Novel Models of Fuzzy Rough Coverings Based on Fuzzy α-Neighborhood and its Application to Decision-Making

Recently, the concept of a fuzzy
$\alpha $
- neighborhood operator with reflexivity was established and a fuzzy rough set covering based on a fuzzy
$\alpha $
- neighborhood operator was defined by Zhang
et al.
As a generalization of Zhang
et al.
models, this article aims to introduce the notion of a complementary fuzzy
$\alpha $
-neighborhood operator with reflexivity. Also, three new kinds of a fuzzy rough set covering based on a fuzzy
$\alpha $
- neighborhood operator are constructed and some of their properties are discussed. Further, the relationships between these models are studied. Several new kinds of a fuzzy rough set covering based variable precision are put forward and the relevant properties are constructed. Finally, an application to MADM to solve realistic problems is illustrated.